Problem: Solve for $x$ and $y$ using elimination. ${-3x-2y = -15}$ ${4x+2y = 16}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-3x-2y = -15}\thinspace$ to find $y$ ${-3}{(1)}{ - 2y = -15}$ $-3-2y = -15$ $-3{+3} - 2y = -15{+3}$ $-2y = -12$ $\dfrac{-2y}{{-2}} = \dfrac{-12}{{-2}}$ ${y = 6}$ You can also plug ${x = 1}$ into $\thinspace {4x+2y = 16}\thinspace$ and get the same answer for $y$ : ${4}{(1)}{ + 2y = 16}$ ${y = 6}$